Method of Strachey

Take a 13x13 magic square and construct the second, third and fourth 13x13 magic square by adding (13 x 13 =) 169, (2 x 169 =
) 338 respectively (3 x 169 = ) 507 to all digits of the first 13x13 magic square. Put the first square in the top left corner, put the second square in the bottom right corner, put the
third square in the top right corner and put the fourth square in the bottom left corner.

93

108

123

138

153

168

1

16

31

46

61

76

91

431

446

461

476

491

506

339

354

369

384

399

414

429

107

122

137

152

167

13

15

30

45

60

75

90

92

445

460

475

490

505

351

353

368

383

398

413

428

430

121

136

151

166

12

14

29

44

59

74

89

104

106

459

474

489

504

350

352

367

382

397

412

427

442

444

135

150

165

11

26

28

43

58

73

88

103

105

120

473

488

503

349

364

366

381

396

411

426

441

443

458

149

164

10

25

27

42

57

72

87

102

117

119

134

487

502

348

363

365

380

395

410

425

440

455

457

472

163

9

24

39

41

56

71

86

101

116

118

133

148

501

347

362

377

379

394

409

424

439

454

456

471

486

8

23

38

40

55

70

85

100

115

130

132

147

162

346

361

376

378

393

408

423

438

453

468

470

485

500

22

37

52

54

69

84

99

114

129

131

146

161

7

360

375

390

392

407

422

437

452

467

469

484

499

345

36

51

53

68

83

98

113

128

143

145

160

6

21

374

389

391

406

421

436

451

466

481

483

498

344

359

50

65

67

82

97

112

127

142

144

159

5

20

35

388

403

405

420

435

450

465

480

482

497

343

358

373

64

66

81

96

111

126

141

156

158

4

19

34

49

402

404

419

434

449

464

479

494

496

342

357

372

387

78

80

95

110

125

140

155

157

3

18

33

48

63

416

418

433

448

463

478

493

495

341

356

371

386

401

79

94

109

124

139

154

169

2

17

32

47

62

77

417

432

447

462

477

492

507

340

355

370

385

400

415

600

615

630

645

660

675

508

523

538

553

568

583

598

262

277

292

307

322

337

170

185

200

215

230

245

260

614

629

644

659

674

520

522

537

552

567

582

597

599

276

291

306

321

336

182

184

199

214

229

244

259

261

628

643

658

673

519

521

536

551

566

581

596

611

613

290

305

320

335

181

183

198

213

228

243

258

273

275

642

657

672

518

533

535

550

565

580

595

610

612

627

304

319

334

180

195

197

212

227

242

257

272

274

289

656

671

517

532

534

549

564

579

594

609

624

626

641

318

333

179

194

196

211

226

241

256

271

286

288

303

670

516

531

546

548

563

578

593

608

623

625

640

655

332

178

193

208

210

225

240

255

270

285

287

302

317

515

530

545

547

562

577

592

607

622

637

639

654

669

177

192

207

209

224

239

254

269

284

299

301

316

331

529

544

559

561

576

591

606

621

636

638

653

668

514

191

206

221

223

238

253

268

283

298

300

315

330

176

543

558

560

575

590

605

620

635

650

652

667

513

528

205

220

222

237

252

267

282

297

312

314

329

175

190

557

572

574

589

604

619

634

649

651

666

512

527

542

219

234

236

251

266

281

296

311

313

328

174

189

204

571

573

588

603

618

633

648

663

665

511

526

541

556

233

235

250

265

280

295

310

325

327

173

188

203

218

585

587

602

617

632

647

662

664

510

525

540

555

570

247

249

264

279

294

309

324

326

172

187

202

217

232

586

601

616

631

646

661

676

509

524

539

554

569

584

248

263

278

293

308

323

338

171

186

201

216

231

246

The columns and the diagonals give already the magic sum. To get the right sum in the rows, you must swap digits, as follows. We split the 13x13 square in the top left corner and the 13x13 square
in the bottom left corner in 'quarters' (marked by the blue digits). The ‘quarters’ top left and bottom left of the 13x13 square in the top left corner must be swapped with the ‘quarters’ top
left and bottom left of the 13x13 square in the bottom left corner. Also the (blue) digits on the border between the two 'quarters’ from the second cell up to the crossing point must be swapped.
Finally the digits of the top half of the last column(s) must be swapped with the digits of the bottom half of the last column(s). Because the digits of the first two columns must be swapped, the
digits of the last (6 – 1 = ) 5 columns must be swapped. See below the result.